The display dimensions of a device, such as an HDTV or a laptop, is usually given as a screen 15" LCD, which is the diagonal size in inches. As I love the metric system and also prefer to think in terms of width and height, I wrote this calculator. It calculates height, width and area of the display, both in inches and centimeters, given its diagonal and aspect ratio.
We know the diagonal size, and we usually know the aspect ratio, which is 4:3 in many cases and 16:19 or 16:9 for wide screens. There are other aspect ratios, which you can choose from the list or add to the list using the handbook Display aspect ratio. If you do not know aspect ratio, or do not want to bother with it, you can enter display dimensions in pixels, and calculator will find out the aspect ratio from width and height in pixels.
Having this data, the logic is simple - the diagonal is converted to centimeters if necessary, and the Pythagorean theorem is used to find the width and height.